Density smoothness estimation problem using a wavelet approach

Karol Dziedziul; Bogdan Ćmiel

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 130-144
  • ISSN: 1292-8100

Abstract

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In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes possible for some classes of the density functions.

How to cite

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Dziedziul, Karol, and Ćmiel, Bogdan. "Density smoothness estimation problem using a wavelet approach." ESAIM: Probability and Statistics 18 (2014): 130-144. <http://eudml.org/doc/273638>.

@article{Dziedziul2014,
abstract = {In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes possible for some classes of the density functions.},
author = {Dziedziul, Karol, Ćmiel, Bogdan},
journal = {ESAIM: Probability and Statistics},
keywords = {estimation; wavelets; Besov spaces; smoothness parameter},
language = {eng},
pages = {130-144},
publisher = {EDP-Sciences},
title = {Density smoothness estimation problem using a wavelet approach},
url = {http://eudml.org/doc/273638},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Dziedziul, Karol
AU - Ćmiel, Bogdan
TI - Density smoothness estimation problem using a wavelet approach
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 130
EP - 144
AB - In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes possible for some classes of the density functions.
LA - eng
KW - estimation; wavelets; Besov spaces; smoothness parameter
UR - http://eudml.org/doc/273638
ER -

References

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